2.5 Digraphs: Walks & Paths

Walks and Paths

  1. Let \(\{a,b,c,d\}\) be four vertices of a directed graph.
    Let \(E(G) = \{(a,b),(a,c),(a,d),(b,c),(b,d),(c,b),(c,d)\}\).
    What is the length of the longest path?

    Exercise 1

    An example of a longest path in this graph is \(a~(a,b)~b~(b,c)~c~(c,d)~d\)

    Recall that the length of a path is defined as the number of edges the path uses.

    Also recall that a path cannot have repeated vertices, so we know this path is (one of) the longest because it uses all the vertices.

  2. If the sum of all the numbers in an adjacency matrix is equal to 6, what does this imply?

    Exercise 2
    The adjacency matrix represents the edges in a digraph.